This document is meant as a tutorial for the first-time user. In this tutorial we walk the user through the different features of the applet with hands-on examples. In doing this, we try to reveal all of the features of the applet. We release this version of the software in hopes that it will be beneficial to its users.

Now, on with the show...

  1. Starting up

    The first thing the user needs to do is to start the applet.

    You could also download the source code from our web-site and compile it yourself. At this point in the tutorial we will assume that you can access the applet and that you have started it.

    Once the applet has loaded, you will see the following screen:

    Opening screen

    The screen has been partitioned into a Menu area, a Control panel, an Input Panel and an Output panel. The screen can be assumed to be partitioned into three rows. Row one has the Menu-Items, row two has the control panel and input panel, row three has the output panel. All the elements have been enclosed in a separate rectangular border for clarity.

    The menu items are used to choose a domain for working, to add a pole/zero, to change the plots in the graph and to view the 3D response graph.

    The control panel helps the user to enter the parameters for changing the various plots and also to change the frequency and bandwidth of a pole/zero.

    The input and output panels display the location of the poles/zeros on the map and their frequency spectra

    The first step in using this tool is to decide whether to work in the digital or the analog domain. By default, it has been set to work in the digital domain.To change the mode of operation,click on the Mode and choose between the Analog and the Digital option.

    In this tutorial we will work exclusively with digital analysis, so change the mode to "Digital" now.

    Now that we have decided which mode of operation to use, we are ready to start with the fun stuff.

  2. Adding/removing the poles and zeros in the system

    Adding a pole or zero is easy. Simply decide what you want the effect of the pole/zero to be (in terms of center frequency and bandwidth). To change the frequency and bandwidth,click on the Parameters and choose the Input option. This will effect a change in the Control panel and have it display the Input Parameters. Then change the value of Frequency and Bandwidth text-fields. To determine whether it should be a pole or zero, click on the Edit menu and choose the Add Pole or the Add Zero option. Let's try this:

    Set Frequency to 0.0 and Bandwidth to 0.07 by typing the respective numbers in each entry field. Click on the "Edit" menu button and then choose the "Add Pole" button. If you did this correctly, your screen should look like this...

    One pole added

    Changing the Sampling Frequency or the DC Gain is also simple. Just choose the Input option in the Parameters menu and change the corresponding text-field entries and press the 'Enter' key on the keyboard.

    Notice that adding this pole has changed virtually every section of the applet. The pole now shows up as a boxed X on the pole/zero map (a zero would show up as a boxed O), the coordinates for the pole are now displayed in the "Poles" list box, and all three output windows are now showing time and frequency responses of the system described by the single pole.

    Let's practice by adding a few more poles and zeros. You can place them wherever you like

    There are two ways to remove the poles and zeros from the system:
    1. You can remove a single pole/zero by clicking on it within the pole/zero map and pressing the button 'd'.

      Try this now with one of the poles or zeros you just created

    2. The second way to remove poles and zeros is to clear the map using the Clear option in the Go menu. This removes all poles and zeros from the system.

      You can try this now, too.

  3. Pole/Zero Manipulation

    There are a few operations available with this applet for manipulating the poles and zeros of the system. The first of which is the use of the mouse to move the pole or zero in the Pole/Zero Map. This is done by clicking on a pole or zero in the Pole/Zero Map and holding the mouse button down while you drag it to another location in the map.

    Create a pole at frequency = 0 and bandwidth = 0.07 with a sample frequency of 1.0. Click on the "X" in the Pole/Zero map denoting this pole. While holding down the mouse button, drag the mouse to a different location in the map. Notice that one or more of the output windows change as you move the mouse. Now release the mouse button and you will see that the output windows now reflect the response of a system to the new pole location.

    In place of the mouse, one could also use keystrokes to move the poles or zeros. This is done by first clicking on the pole or zero you desire to move and then using the "i", "j", "k" and "l" keys for movement up, left, down, and right respectively.

    Try this!

    One of the more important features of the pole zero map is the ability to create conjugate pairs and to treat them as a singular object. To create a conjugate pair you must first create a single pole or zero. Next, click on that pole or zero in the Pole/Zero Map and press the "c" key. You can then move the pair around just as you would a singular pole or zero.

    First clear the map(you know how to do this). Now create a pole at frequency = 0.12 and bandwidth = 0.07. Now click on that pole and hit the "c" key. You should now have two poles, one at frequency = 0.12, bandwidth = 0.07, and one at frequency = -0.12, bandwidth = 0.07. Try dragging one of them with the mouse and see that the other "follows".

    A conjugate pole pair

  4. System Response Windows

    There are (4) response types which are available with this applet They are: Impulse response, Magnitude response, Phase response, and 3-Dimensional Magnitude response. The Impulse, Magnitude and Phase response windows are located at the bottom of the applet screen from left-to-right respectively. The 3-D response window is separate from the applet main window and can be accessed from the choosing the Frequency Response option in the Go menu. What follows will show how to use the various output windows.